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The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams

Guido Rizzi, Matteo Luca Ruggiero

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a formal analogy with the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and Newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a formal analogy with the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and Newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.

Jan 1, 200315 citations

A note on the Sagnac effect for matter beams

Matteo Luca Ruggiero, Angelo Tartaglia

arXiv:1411.0135The European Physical Journal PlusMay 1, 201514 citations

Initial Phase Dependence of the Sagnac Effect for Matter Waves

Martin C. Kandes, M. W. J. Bromley, R. Carretero-González

Bulletin of the American Physical SocietyJun 6, 20170 citations

Sagnac effect as viewed by a co-rotating observer

B H W Hendricks, Gerard Nienhuis

The authors consider the Sagnac effect from the point of view of a co-rotating observer. They give for both matter and light waves the fully relativistic evolution equations in the rotating frame of reference. In the nonrelativistic limit the Sagnac effect is similar to the Aharonov-Bohm effect. This similarity shows that the Sagnac effect is a manifestation of Berry's phase.

Quantum Optics Journal of the European Optical Society Part BFeb 1, 199020 citations

Relativistic corrections to the Aharonov-Bohm scattering

M. Gomes, J. M. C. Malbouisson, A. J. da Silva

arXiv:hep-th/9611027Physics Letters ADec 1, 199714 citations

Substratum Interpretation of the Sagnac-and the Aharonov-Bohm Effect

Friedwardt Winterberg

Abstract It is shown that a substratum interpretation reveals a close relationship between the Sagnac- and the Aharonov-Bohm-effect. The characteristic peculiarity of the Aharonov-Bohm-effect, to produce a phase shift of the electron wave function even in the absence of any electromagnetic force fields, can be duplicated by a thought experiment for light waves in the gravitational field of a massive rotating cylinder, which demonstrates that the somewhat similar Sagnac-effect is not caused by centrifugal and Corioli’s forces, as it is sometimes claimed. In the substratum interpretation, both the Sagnac and Aharonov-Bohm effect find their explanation in a rotational motion of the substratum. If the substratum flow is irrotational, having the form of a potential vortex, these effects persist even though there are no force fields present.Abstract It is shown that a substratum interpretation reveals a close relationship between the Sagnac- and the Aharonov-Bohm-effect. The characteristic peculiarity of the Aharonov-Bohm-effect, to produce a phase shift of the electron wave function even in the absence of any electromagnetic force fields, can be duplicated by a thought experiment for light waves in the gravitational field of a massive rotating cylinder, which demonstrates that the somewhat similar Sagnac-effect is not caused by centrifugal and Corioli’s forces, as it is sometimes claimed. In the substratum interpretation, both the Sagnac and Aharonov-Bohm effect find their explanation in a rotational motion of the substratum. If the substratum flow is irrotational, having the form of a potential vortex, these effects persist even though there are no force fields present.

Zeitschrift für Naturforschung ADec 1, 19895 citations

The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams

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The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams

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